$\dfrac{ -3d - 5e }{ 7 } = \dfrac{ -8d - 3f }{ -2 }$ Solve for $d$.
Multiply both sides by the left denominator. $\dfrac{ -3d - 5e }{ {7} } = \dfrac{ -8d - 3f }{ -2 }$ ${7} \cdot \dfrac{ -3d - 5e }{ {7} } = {7} \cdot \dfrac{ -8d - 3f }{ -2 }$ $-3d - 5e = {7} \cdot \dfrac { -8d - 3f }{ -2 }$ Multiply both sides by the right denominator. $-3d - 5e = 7 \cdot \dfrac{ -8d - 3f }{ -{2} }$ $-{2} \cdot \left( -3d - 5e \right) = -{2} \cdot 7 \cdot \dfrac{ -8d - 3f }{ -{2} }$ $-{2} \cdot \left( -3d - 5e \right) = 7 \cdot \left( -8d - 3f \right)$ Distribute both sides $-{2} \cdot \left( -3d - 5e \right) = {7} \cdot \left( -8d - 3f \right)$ ${6}d + {10}e = -{56}d - {21}f$ Combine $d$ terms on the left. ${6d} + 10e = -{56d} - 21f$ ${62d} + 10e = -21f$ Move the $e$ term to the right. $62d + {10e} = -21f$ $62d = -21f - {10e}$ Isolate $d$ by dividing both sides by its coefficient. ${62}d = -21f - 10e$ $d = \dfrac{ -21f - 10e }{ {62} }$